A separation membrane module using a separation membrane with selective permeability for gas separation (for example, separation of oxygen, nitrogen, hydrogen, water vapor, carbon dioxide, organic vapor or the like) can be of plate and frame type, of tubular type, of hollow fiber type or the like. Among these, a hollow-fiber type gas separation membrane module is industrially excellent because it is not only advantageous in its largest membrane area per a unit volume but also superior in pressure resistance and self-supporting ability, and thus has been extensively used.